A microbial strain is cultured in a 100 L stirred fermenter for secondary metabolite
production. If the specific rate of oxygen uptake is 0.4 h-1 and the oxygen solubility in the
broth is 8 mg/L, then the volumetric mass transfer coefficient (KLa) (in s-1) of oxygen
required to achieve a maximum cell concentration of 12 g/L is (up to two decimal
places) _________
Official Answer Key:
0.16 to 0.17
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.56)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"A microbial strain is cultured in a 100 L stirred fermenter for secondary metabolite
production. If the specific rate of oxygen uptake is 0.4 h-1 and the oxygen solubility in the
broth is 8 mg/L, then the volumetric mas..."*
- Identifying governing bioprocess / mathematical relation:
- Evaluating volumetric mass transfer rate for oxygen in aerobic fermentation:
$\text{OTR} = k_L a (C^* - C_L)$
where $k_L a$ is volumetric mass transfer coefficient, $C^*$ is equilibrium saturation dissolved oxygen concentration, and $C_L$ is actual bulk liquid concentration.
- **Calculated Quantitative Value**: **0.16 to 0.17**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **0.16 to 0.17**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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